Pearson Edexcel International A Level · Mathematics (YMA01)

Trigonometry: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Trigonometry.

10 questions29 marksFree, no account

Question 1

1 mark

A sector of a circle has a radius of \( 6 \) cm and a central angle of \( \frac{2\pi}{3} \) radians. Calculate the area of the sector in terms of \( \pi \).

Question 2

1 mark

Given that \( \tan \theta + \cot \theta = 4 \) and \( 0 < \theta < \frac{\pi}{4} \), find the exact value of \( \cos 2\theta \).

Question 3

1 mark

Find all values of \( x \) in the interval \( 0^\circ \le x < 360^\circ \) that satisfy the equation:
\( 2\cos^2 x - \sin x - 1 = 0 \)

Question 4

1 mark

In triangle \( ABC \), side \( AB = (x + 3) \) cm, side \( BC = (2x + 4) \) cm, and side \( AC = 7 \) cm. Given that angle \( \angle ABC = 60^\circ \), find the area of the triangle.

Question 5

1 mark

A sector of a circle has radius \( r \) cm and a central angle of \( \theta \) radians. The perimeter of the sector is fixed at \( 24 \) cm. Find the value of \( \theta \) that results in the maximum possible area for the sector.

Question 6

2 marks

In triangle \( ABC \), side \( AB = 8 \text{ cm} \), side \( BC = 11 \text{ cm} \) and angle \( \angle ABC = 150^\circ \). Calculate the area of the triangle, giving your answer in \( \text{cm}^2 \).

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Question 7

5 marks

In triangle \( ABC \), \( AB = 5 \text{ cm} \), \( AC = 7 \text{ cm} \), and angle \( \angle ABC = 60^\circ \). Given that \( BC = x \text{ cm} \), find the value of \( x \) by forming and solving a quadratic equation.

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Question 8

6 marks

In triangle \( ABC \), side \( a = 7 \text{ cm} \), side \( b = 5 \text{ cm} \) and the area of the triangle is \( 10\sqrt{3} \text{ cm}^2 \). Find the two possible exact lengths of side \( c \).
[6 marks]

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Question 9

5 marks

(a) Express \(2\sin \theta + 5\cos \theta\) in the form \(R\sin(\theta + \alpha)\), where \(R > 0\) and \(0 < \alpha < 90^\circ\). Give the value of \(\alpha\) to 2 decimal places.
(b) Hence, solve the equation \(2\sin \theta + 5\cos \theta = 3\) for \(0 \le \theta < 360^\circ\), giving your answers to one decimal place.
(c) Write down the maximum value of \(2\sin \theta + 5\cos \theta\) and the smallest positive value of \(\theta\) at which this maximum occurs.

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Question 10

6 marks

(a) Show that the equation \(3\cos 2\theta + \sin \theta = 2\) can be written in the form \(6\sin^2 \theta - \sin \theta - 1 = 0\).
(b) Hence solve, for \(0 \le \theta < 360^\circ\), the equation \(3\cos 2\theta + \sin \theta = 2\), giving your answers to one decimal place where appropriate.

Write your answer out first, then check it against the worked solution.

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